q-Rung Orthopair Picture Fuzzy Topological Spaces and Parameter-Dependent Continuity: Control System Applications

This paper presents novel concepts in fuzzy topologies, namely q-rung orthopair picture fuzzy (q-ROPF) topology and q-rung orthopair picture fuzzy point (q-ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called qε-ROPF contin...

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Veröffentlicht in:Mathematical problems in engineering Jg. 2023; H. 1
Hauptverfasser: Ünver, Mehmet, Olgun, Murat
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Hindawi 2023
John Wiley & Sons, Inc
Schlagworte:
Continuity (mathematics)
Control systems
Fuzzy sets
Investigations
Mathematical problems
Neighborhoods
Robust control
Set theory
Topology
ISSN:1024-123X, 1563-5147
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Zusammenfassung:This paper presents novel concepts in fuzzy topologies, namely q-rung orthopair picture fuzzy (q-ROPF) topology and q-rung orthopair picture fuzzy point (q-ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called qε-ROPF continuity, which allows for a flexible analysis of functions between q-ROPF topological spaces by incorporating an error bound ε. We define the q-neighborhood system for a q-ROPF point in a q-ROPF topological space and investigate the convergence of sequences of such points. Our results shed light on the behavior of functions and sequences in these spaces, as well as the conditions for uniqueness of limits within the realm of supports. This research has practical implications in control systems, providing valuable insights into the stability and robustness of the control strategies in the presence of small changes represented by the epsilon value.
Bibliographie:ObjectType-Article-1
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ISSN:1024-123X
1563-5147
DOI:10.1155/2023/8848196